# Properties

 Label 9900.w Number of curves 2 Conductor 9900 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9900.w1")

sage: E.isogeny_class()

## Elliptic curves in class 9900.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9900.w1 9900k2 [0, 0, 0, -2775, 26750]  12288
9900.w2 9900k1 [0, 0, 0, 600, 3125]  6144 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9900.w have rank $$1$$.

## Modular form9900.2.a.w

sage: E.q_eigenform(10)

$$q + 2q^{7} - q^{11} + 2q^{13} + 4q^{17} - 6q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 